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International Journal of Quantum Chemistry

Effective error correction method for quantum information processing

Minaru Kawamura, Takuji Morimoto, Yoshiyuki Mori, Ryuichi Sawae, Kenichi Takarabe, Yoshinori Manmoto, Toshio Sakata

Published Jan 1, 2007• 1 citation
Publisher

Abstract

Abstract In this paper we present an effective error correction method to correct the errors that occur during quantum information processing. (There are various methods of quantum error correction such as error correcting code or decoherence free subspace which protect quantum information from noise, and they are useful for storage and communication; however, it would be difficult to adapt them to quantum information processing practically.) In this method the error detection is carried out through the asymmetry or the irreversibility of quantum computers, which ought to be inherently symmetric and reversible. The irreversibility is usually caused by decoherence and dissipation, and the processing's own adjoint operator can, therefore, be used to condense such errors and enable their detection. The effectiveness of this method is investigated with an NMR quantum computer. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007

DOI
10.1002/qua.21450

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Abstract In this paper we present an effective error correction method to correct the errors that occur during quantum information processing. (There are various methods of quantum error correction such as error correcting code or decoherence free subspace which protect quantum information from noise, and they are useful for storage and communication; however, it would be difficult to adapt them to quantum information processing practically.) In this method the error detection is carried out through the asymmetry or the irreversibility of quantum computers, which ought to be inherently symmetric and reversible. The irreversibility is usually caused by decoherence and dissipation, and the processing's own adjoint operator can, therefore, be used to condense such errors and enable their detection. The effectiveness of this method is investigated with an NMR quantum computer. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007
Quantum error correction is a set of methods to protect quantum information--that is, quantum states--from unwanted environmental interactions (decoherence) and other forms of noise. The information is stored in a quantum error-correcting code, which is a subspace in a larger Hilbert space. This code is designed so that the most common errors move the state into an error space orthogonal to the original code space while preserving the information in the state. It is possible to determine whether an error has occurred by a suitable measurement and to apply a unitary correction that returns the state to the code space, without measuring (and hence disturbing) the protected state itself. In general, codewords of a quantum code are entangled states. No code that stores information can protect against all possible errors; instead, codes are designed to correct a specific error set, which should be chosen to match the most likely types of noise. An error set is represented by a set of operators that can multiply the codeword state. Quantum error correction is used to protect information in quantum communication (where quantum states pass through noisy channels) and quantum computation (where quantum states are transformed through a sequence of imperfect computational steps in the presence of environmental decoherence to solve a computational problem). In quantum computation, error correction is just one component of fault-tolerant design.
Quantum technologies have shown immeasurable potential to effectively solve several information processing tasks such as prime number factorization, unstructured database search or complex macromolecule simulation. As a result of such capability to solve certain problems that are not classically tractable, quantum machines have the potential revolutionize the modern world via applications such as drug design, process optimization, unbreakable communications or machine learning. However, quantum information is prone to suffer from errors caused by the so-called decoherence, which describes the loss in coherence of quantum states associated to their interactions with the surrounding environment. This decoherence phenomenon is present in every quantum information task, be it transmission, processing or even storage of quantum information. Consequently, the protection of quantum information via quantum error correction codes (QECC) is of paramount importance to construct fully operational quantum computers. Understanding environmental decoherence processes and the way they are modeled is fundamental in order to construct effective error correction methods capable of protecting quantum information. In this thesis, the nature of decoherence is studied and mathematically modelled; and QECCs are designed and optimized so that they exhibit better error correction capabilities.
Quantum error correction is a set of methods to protect quantum information--that is, quantum states--from unwanted environmental interactions (decoherence) and other forms of noise. The information is stored in a quantum error-correcting code, which is a subspace in a larger Hilbert space. This code is designed so that the most common errors move the state into an error space orthogonal to the original code space while preserving the information in the state. It is possible to determine whether an error has occurred by a suitable measurement and to apply a unitary correction that returns the state to the code space, without measuring (and hence disturbing) the protected state itself. In general, codewords of a quantum code are entangled states. No code that stores information can protect against all possible errors; instead, codes are designed to correct a specific error set, which should be chosen to match the most likely types of noise. An error set is represented by a set of operators that can multiply the codeword state. Quantum error correction is used to protect information in quantum communication (where quantum states pass through noisy channels) and quantum computation (where quantum states are transformed through a sequence of imperfect computational steps in the presence of environmental decoherence to solve a computational problem). In quantum computation, error correction is just one component of fault-tolerant design.
Quantum error correction plays a vital role in the Quantum information process. Nowadays, the research has been increased in quantum technology and is being applied in various applications like secure communications, finance, machine learning, drug analysis and etc. But the quantum information process is difficult compared to the classical due to the challenges in quantum technology like no-cloning theorem, decoherence, and the difficulty in quantum states measurement. Thus the error rate is high and it is not possible to build a quantum computer without an error detection and correction mechanism. In this paper, we are discussing various error correction methods and proposing a novel encoding method for quantum error correction.
The field of quantum computing holds immense promise for solving complex problems that are currently intractable for classical computers. However, the practical realization of quantum computers faces a critical challenge: the inherent fragility of qubits, the fundamental units of quantum information. Quantum systems are susceptible to various types of errors and decoherence due to their interaction with the surrounding environment, which can lead to a rapid degradation of quantum information. This chapter delves into the pivotal aspect of quantum error correction techniques as a means to mitigate the adverse effects of errors and decoherence in quantum computing systems. Begins by elucidating the theoretical foundations of quantum error correction, exploring the principles that underlie the encoding of quantum information into larger, redundant codes that are resilient to errors. A comprehensive overview of prominent quantum error correction codes, such as the stabilizer codes and topological codes, is provided, along with a discussion of their respective strengths and limitations.
Abstract Intensive research is currently being carried out to develop and create quantum computers and their software. This work is devoted to study of the influence of the environment on the quantum system of qubits. Quantum error correction is a set of methods for protecting quantum information and quantum state from unwanted interactions of the environment (decoherence) and other forms and types of noise. The article discusses the solution to the problem of research and development of corrective codes for rectifying several types of quantum errors that occur during computational processes in quantum algorithms and models of quantum computing devices. The aim of the work is to study existing methods for correcting various types of quantum errors and to create a corrective code for quantum error rectification. The scientific novelty is expressed in the exclusion of one of the shortcomings of the quantum computing process.